Question

The graph of the function f is shown below with domain [-12, 10]. Let g(x)=integral[-12,x] f(t)dt.

desmos calculator code: calculator/jycetemxr2 (add desmos url)

A. Evaluate g(0), g'(0), and g''(0).

B. Find all possible values of x such that g(x) = 0. Justify your answer.

C. Determine where the graph of g(x) has horizontal tangent lines, if anywhere. Justify your answer.

Answer 1

If you can't get to the graph, the points are (-12, 5), (-10, 5), (0, -5), (2, -5), (6, 5), and (10, 5). These points are connected with straight lines only, in order.